As a freshman at Texas in 2016, Shugart made 32 appearances, all in relief, and pitched to a 2–3 record and 4.53 ERA.[4] In 2017, as a sophomore, he was 3–2 with a 3.43 ERA and 1.45 WHIP in 42 innings pitched out of the bullpen.[5] After the season, he pitched for the Cotuit Kettleers of the Cape Cod Baseball League.[6][7] Shugart transitioned from a reliever to a starting pitcher as a junior in 2018.[8][9] He pitched for Texas in the 2018 College World Series until the Longhorns were eliminated by the Florida Gators on June 19.[10] He finished his junior year with a 5–3 record and a 4.36 ERA in 84+2⁄3 innings pitched.[11]
On March 22, 2019, MLB suspended Shugart for fifty games after a second positive test for a drug of abuse.[17][18] Shugart subsequently made his first appearance of the 2019 season on May 27 with the Greenville Drive of the Single-ASouth Atlantic League,[16] spending the remainder of the year there. Over 16 starts, Shugart went 6–4 with a 2.81 ERA, striking out 73 over 89+2⁄3 innings.[16] After the 2020 minor league season was cancelled due to the COVID-19 pandemic, Shugart was invited to participate in the Red Sox' fall instructional league.[19] For the 2021 season, Shugart returned to Greenville, now members of the High-A East, started 22 games and pitched to a 6–6 record, a 4.78 ERA, and 93 strikeouts over 105+1⁄3 innings.[20] He opened the 2022 season with the Portland Sea Dogs of the Double-AEastern League and moved into the bullpen.[21] In early July, he was promoted to the Worcester Red Sox of the Triple-AInternational League.[22] On August 4, he pitched two innings of a combined no-hitter alongside Michael Wacha and Andrew Politi versus the Durham Bulls.[23] Over 45 games (one start) between the two affiliates, Shugart went 5–5 with a 5.31 ERA and 63 strikeouts over 62+2⁄3 innings.[24]
Shugart spent the entirety of the 2023 season with Triple–A Worcester. In 40 appearances with the club, he struggled to an 8.22 ERA with 39 strikeouts and 4 saves over 46 innings pitched.[25] He returned to Worcester to begin the 2024 campaign.
On August 12, 2024, Shugart was selected to the 40-man roster and promoted to the major leagues for the first time.[26] In 6 games for Boston, he logged a 4.15 ERA with 8 strikeouts and 1 save across 8+2⁄3 innings pitched. Shugart was designated for assignment following the acquisition of Blake Sabol on January 15, 2025.[27]
Pittsburgh Pirates
On January 17, 2025, Shugart was traded to the Pittsburgh Pirates in exchange for Matt McShane.[28] He was optioned to the Triple-A Indianapolis Indians to begin the season.[29] On April 22, Shugart recorded his first career win after tossing two scoreless innings against the Los Angeles Angels.[30] In 35 appearances for Pittsburgh, he compiled a 4-3 record and 3.40 ERA with 31 strikeouts over 45 innings of work. On January 8, 2026, Shugart was designated for assignment following the signing of Ryan O'Hearn.[31]
Shugart was called up to the Phillies on April 14.[34] In a doubleheader against the San Francisco Giants on April 30, Shugart accomplished the rare feat of recording the win in both games, becoming the first pitcher to do so since 2013.[35]